Finite Group Databasebeta

← C37×#10745 #22631998

Subgroups — C37×#10745 #22631998

Order 9472.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#518C211yesmaximal, characteristic
2C22×#99×C37C211yesmaximal, characteristic
3C2×C37×#386C211yesmaximal, characteristic
4C2×C37×#342C212yesmaximal, complemented
5C37×C22⋊#95C212yesmaximal, complemented
6C23×D4×C37C2211yescharacteristic
7C24×C4×C37C2211yescharacteristic
8C37×#518—22no—
9C37×#518—24no—
10C37×#518C414yescomplemented
11C2×C4×D4×C37—24no—
12C2×#117×C37—21no—
13C22×C22⋊C4×C37—21no—
14C22×C22⋊C4×C37—21no—
15C22×C22⋊C4×C37C2212yes—
16C22×C22⋊C4×C37C2211yescharacteristic
17C22×C22⋊C4×C37C2212yes—
18C2×#99×C37—22no—
19C2×#99×C37—22no—
20C2×#99×C37C414yescomplemented
21C37×#386—22no—
22C37×#386C414yescomplemented
23C2×#95×C37—21no—
24C2×#95×C37—24no—
25C37×#342—24no—
26C25×C37D411yescharacteristic
27C25×C37C2311yescharacteristic
28C22×D4×C37—22no—
29C22×D4×C37—22no—
30C22×D4×C37—22no—
31C22×D4×C37—22no—
32C22×D4×C37C2×C412yes—
33C22×D4×C37C2×C412yes—
34C22×D4×C37C2×C412yes—
35C22×D4×C37D412yes—
36C22×D4×C37D412yes—
37C22×D4×C37Q812yes—
38C23×C4×C37—22no—
39C23×C4×C37—21no—
40C23×C4×C37—22no—
41C23×C4×C37—21no—
42C23×C4×C37—22no—
43C23×C4×C37—21no—
44C23×C4×C37—22no—
45C23×C4×C37—44no—
46C23×C4×C37C2×C412yescomplemented
47C23×C4×C37D411yescharacteristic
48C23×C4×C37D414yes—
49C4×D4×C37—216no—
50C4×D4×C37—216no—
51#117×C37—24no—
52#117×C37—24no—
53C2×C4⋊C4×C37—22no—
54C2×C22⋊C4×C37—22no—
55C2×C22⋊C4×C37—24no—
56C2×C22⋊C4×C37—24no—
57C2×C22⋊C4×C37—22no—
58C2×C22⋊C4×C37—22no—
59C2×C22⋊C4×C37—22no—
60C2×C22⋊C4×C37—22no—
61C2×C22⋊C4×C37—22no—
62C2×C22⋊C4×C37—22no—
63C2×C22⋊C4×C37—22no—
64C2×C22⋊C4×C37—22no—
65C2×C22⋊C4×C37—22no—
66C2×C22⋊C4×C37—22no—
67C2×C22⋊C4×C37—24no—
68C2×C22⋊C4×C37—21no—
69C2×C22⋊C4×C37—22no—
70C2×C22⋊C4×C37—44no—
71C2×C22⋊C4×C37C2×C414yes—
72C2×C22⋊C4×C37C2×C412yescomplemented
73C2×C22⋊C4×C37C2×C414yescomplemented
74C2×C22⋊C4×C37D414yes—
75C2×C42×C37—22no—
76#99×C37—28no—
77#95×C37—24no—
78#95×C37—48no—
79C24×C37—21no—
80C24×C37—21no—
81C24×C37—21no—
82C24×C37—21no—
83C24×C37—42no—
84C24×C37—42no—
85C24×C37—42no—
86C24×C37—42no—
87C24×C37C22⋊C412yes—
88C24×C37C22⋊C412yes—
89C24×C37C4⋊C412yes—
90C24×C37C22×C411yescharacteristic
91C24×C37C22×C411yescharacteristic
92C24×C37C22×C411yescharacteristic
93C24×C37C2×D411yescharacteristic
94C24×C37C2×D412yes—
95C24×C37C2×D411yescharacteristic
96C24×C37C2×D411yescharacteristic
97C24×C37C2×D412yes—
98C24×C37C2×Q811yescharacteristic
99C24×C37#4112yes—
100C24×C37#4112yes—
101C2×D4×C37—24no—
102C2×D4×C37—24no—
103C2×D4×C37—24no—
104C2×D4×C37—24no—
105C2×D4×C37—24no—
106C2×D4×C37—24no—
107C2×D4×C37—24no—
108C2×D4×C37—24no—
109C2×D4×C37—24no—
110C2×D4×C37—24no—
111C2×D4×C37—24no—
112C2×D4×C37—24no—
113C2×D4×C37C4214yes—
114C2×D4×C37C22⋊C414yes—
115C2×D4×C37C4⋊C414yes—
116C2×D4×C37C4⋊C414yes—
117C22×C4×C37—21no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—28no—
122C22×C4×C37—24no—
123C22×C4×C37—22no—
124C22×C4×C37—24no—
125C22×C4×C37—24no—
126C22×C4×C37—28no—
127C22×C4×C37—24no—
128C22×C4×C37—22no—
129C22×C4×C37—24no—
130C22×C4×C37—44no—
131C22×C4×C37—44no—
132C22×C4×C37—48no—
133C22×C4×C37—44no—
134C22×C4×C37—42no—
135C22×C4×C37—41no—
136C22×C4×C37—42no—
137C22×C4×C37—41no—
138C22×C4×C37—44no—
139C22×C4×C37—44no—
140C22×C4×C37—44no—
141C22×C4×C37—42no—
142C22×C4×C37—44no—
143C22×C4×C37—42no—
144C22×C4×C37—41no—
145C22×C4×C37—42no—
146C22×C4×C37—42no—
147C22×C4×C37—41no—
148C22×C4×C37—82no—
149C22×C4×C37—82no—
150C22×C4×C37C22⋊C412yes—
151C22×C4×C37C22⋊C412yes—
152C22×C4×C37C22⋊C418yescomplemented
153C22×C4×C37C4⋊C412yes—
154C4⋊C4×C37—28no—
155C22⋊C4×C37—28no—
156C22⋊C4×C37—24no—
157C22⋊C4×C37—24no—
158C22⋊C4×C37—24no—
159C22⋊C4×C37—24no—
160C22⋊C4×C37—24no—
161C22⋊C4×C37—24no—
162C22⋊C4×C37—24no—
163C22⋊C4×C37—48no—
164C22⋊C4×C37—42no—
165C22⋊C4×C37—42no—
166C22⋊C4×C37—42no—
167C42×C37—28no—
168C23×C37—24no—
169C23×C37—22no—
170C23×C37—24no—
171C23×C37—22no—
172C23×C37—22no—
173C23×C37—22no—
174C23×C37—22no—
175C23×C37—22no—
176C23×C37—22no—
177C23×C37—22no—
178C23×C37—41no—
179C23×C37—41no—
180C23×C37—42no—
181C23×C37—42no—
182C23×C37—41no—
183C23×C37—42no—
184C23×C37—41no—
185C23×C37—44no—
186C23×C37—42no—
187C23×C37—42no—
188C23×C37—44no—
189C23×C37—42no—
190C23×C37—42no—
191C23×C37—42no—
192C23×C37—44no—
193C23×C37—44no—
194C23×C37—42no—
195C23×C37—42no—
196C23×C37—82no—
197C23×C37—81no—
198C23×C37—81no—
199C23×C37—82no—
200C23×C37#9514yescomplemented
201C23×C37C2×C4211yescharacteristic
202C23×C37C2×C22⋊C411yescharacteristic
203C23×C37C2×C22⋊C411yescharacteristic
204C23×C37C2×C22⋊C412yes—
205C23×C37C2×C22⋊C411yescharacteristic
206C23×C37C2×C4⋊C411yescharacteristic
207C23×C37C2×C4⋊C411yescharacteristic
208C23×C37C2×C4⋊C411yescharacteristic
209C23×C37#11712yes—
210C23×C37C4×D412yes—
211C23×C37C4×D412yes—
212C23×C37C4×D412yes—
213C23×C37C4×D412yes—
214C23×C37#12011yescharacteristic
215C23×C37#12012yes—
216C23×C37#12011yescharacteristic
217C23×C37#12112yes—
218C23×C37#12112yes—
219C23×C37C22⋊Q812yes—
220C23×C37C22⋊Q812yes—
221C23×C37#12311yescharacteristic
222C23×C37#12311yescharacteristic
223C23×C37#12312yes—
224D4×C37—28no—
225D4×C37—28no—
226D4×C37—28no—
227D4×C37—28no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—24no—
235C2×C4×C37—28no—
236C2×C4×C37—28no—
237C2×C4×C37—42no—
238C2×C4×C37—44no—
239C2×C4×C37—48no—
240C2×C4×C37—44no—
241C2×C4×C37—42no—
242C2×C4×C37—44no—
243C2×C4×C37—44no—
244C2×C4×C37—44no—
245C2×C4×C37—48no—
246C2×C4×C37—42no—
247C2×C4×C37—48no—
248C2×C4×C37—42no—
249C2×C4×C37—42no—
250C2×C4×C37—44no—
251C2×C4×C37—84no—
252C2×C4×C37—88no—
253C2×C4×C37—82no—
254C2×C4×C37—82no—
255C2×C4×C37—82no—
256C2×C4×C37—84no—
257C2×C4×C37—82no—
258C2×C4×C37#9514yescomplemented
259#10745C3711yesmaximal, characteristic, direct product factor, Sylow
260C22×C37—24no—
261C22×C37—22no—
262C22×C37—22no—
263C22×C37—24no—
264C22×C37—21no—
265C22×C37—22no—
266C22×C37—22no—
267C22×C37—21no—
268C22×C37—21no—
269C22×C37—22no—
270C22×C37—21no—
271C22×C37—22no—
272C22×C37—24no—
273C22×C37—24no—
274C22×C37—22no—
275C22×C37—22no—
276C22×C37—24no—
277C22×C37—41no—
278C22×C37—41no—
279C22×C37—41no—
280C22×C37—41no—
281C22×C37—42no—
282C22×C37—42no—
283C22×C37—42no—
284C22×C37—42no—
285C22×C37—42no—
286C22×C37—42no—
287C22×C37—44no—
288C22×C37—44no—
289C22×C37—42no—
290C22×C37—42no—
291C22×C37—44no—
292C22×C37—82no—
293C22×C37—82no—
294C22×C37—82no—
295C22×C37C2×#9511yescharacteristic
296C22×C37C4×C22⋊C412yes—
297C22×C37#37911yescharacteristic
298C22×C37#38012yes—
299C22×C37#38111yescharacteristic
300C22×C37#38511yescharacteristic
301C22×C37#38512yes—
302C22×C37#38511yescharacteristic
303C22×C37#38611yescharacteristic
304C22×C37#38612yes—
305C22×C37#38611yescharacteristic
306C22×C37B(4,𝔽2)12yes—
307C22×C37#45812yes—
308C4×C37—24no—
309C4×C37—44no—
310C4×C37—48no—
311C4×C37—82no—
312C4×C37—84no—
313C2×#518C2×C3711yescharacteristic
314C22×#99C2×C3711yescharacteristic
315C2×#386C2×C3711yescharacteristic
316C2×#342C2×C3712yescomplemented
317C22⋊#95C2×C3712yescomplemented
318C2×C37—21no—
319C2×C37—22no—
320C2×C37—21no—
321C2×C37—21no—
322C2×C37—21no—
323C2×C37—22no—
324C2×C37—22no—
325C2×C37—22no—
326C2×C37—44no—
327C2×C37C22⋊#9511yescharacteristic
328C2×C37#179012yes—
329C2×C37#186712yes—
330C2×C37#188911yescharacteristic
331C2×C37#189011yescharacteristic
332C23×D4C22×C3711yescharacteristic
333C24×C4C22×C3711yescharacteristic
334#518—22no—
335#518—24no—
336#518C4×C3714yescomplemented
337C2×C4×D4—24no—
338C2×#117—21no—
339C22×C22⋊C4—21no—
340C22×C22⋊C4—21no—
341C22×C22⋊C4C22×C3712yes—
342C22×C22⋊C4C22×C3711yescharacteristic
343C22×C22⋊C4C22×C3712yes—
344C2×#99—22no—
345C2×#99—22no—
346C2×#99C4×C3714yescomplemented
347#386—22no—
348#386C4×C3714yescomplemented
349C2×#95—21no—
350C2×#95—24no—
351#342—24no—
352C37#1074511yescharacteristic, direct product factor, Sylow
353C25D4×C3711yescharacteristic
354C25C23×C3711yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C3712yes—
360C22×D4C2×C4×C3712yes—
361C22×D4C2×C4×C3712yes—
362C22×D4D4×C3712yes—
363C22×D4D4×C3712yes—
364C22×D4Q8×C3712yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—44no—
373C23×C4C2×C4×C3712yescomplemented
374C23×C4D4×C3711yescharacteristic
375C23×C4D4×C3714yes—
376C4×D4—216no—
377C4×D4—216no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×C4×C3714yes—
399C2×C22⋊C4C2×C4×C3712yescomplemented
400C2×C22⋊C4C2×C4×C3714yescomplemented
401C2×C22⋊C4D4×C3714yes—
402C2×C42—22no—
403#99—28no—
404#95—24no—
405#95—48no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C3712yes—
415C24C22⋊C4×C3712yes—
416C24C4⋊C4×C3712yes—
417C24C22×C4×C3711yescharacteristic
418C24C22×C4×C3711yescharacteristic
419C24C22×C4×C3711yescharacteristic
420C24C2×D4×C3711yescharacteristic
421C24C2×D4×C3712yes—
422C24C2×D4×C3711yescharacteristic
423C24C2×D4×C3711yescharacteristic
424C24C2×D4×C3712yes—
425C24C2×Q8×C3711yescharacteristic
426C24#41×C3712yes—
427C24#41×C3712yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C3714yes—
441C2×D4C22⋊C4×C3714yes—
442C2×D4C4⋊C4×C3714yes—
443C2×D4C4⋊C4×C3714yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C3712yes—
478C22×C4C22⋊C4×C3712yes—
479C22×C4C22⋊C4×C3718yescomplemented
480C22×C4C4⋊C4×C3712yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—44no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—81no—
525C23—81no—
526C23—82no—
527C23#95×C3714yescomplemented
528C23C2×C42×C3711yescharacteristic
529C23C2×C22⋊C4×C3711yescharacteristic
530C23C2×C22⋊C4×C3711yescharacteristic
531C23C2×C22⋊C4×C3712yes—
532C23C2×C22⋊C4×C3711yescharacteristic
533C23C2×C4⋊C4×C3711yescharacteristic
534C23C2×C4⋊C4×C3711yescharacteristic
535C23C2×C4⋊C4×C3711yescharacteristic
536C23#117×C3712yes—
537C23C4×D4×C3712yes—
538C23C4×D4×C3712yes—
539C23C4×D4×C3712yes—
540C23C4×D4×C3712yes—
541C23#120×C3711yescharacteristic
542C23#120×C3712yes—
543C23#120×C3711yescharacteristic
544C23#121×C3712yes—
545C23#121×C3712yes—
546C23C22⋊Q8×C3712yes—
547C23C22⋊Q8×C3712yes—
548C23#123×C3711yescharacteristic
549C23#123×C3711yescharacteristic
550C23#123×C3712yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—84no—
584C2×C4—82no—
585C2×C4#95×C3714yescomplemented
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—21no—
591C22—22no—
592C22—22no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—22no—
598C22—24no—
599C22—24no—
600C22—22no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—44no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×#95×C3711yescharacteristic
622C22C4×C22⋊C4×C3712yes—
623C22C37×#37911yescharacteristic
624C22C37×#38012yes—
625C22C37×#38111yescharacteristic
626C22C37×#38511yescharacteristic
627C22C37×#38512yes—
628C22C37×#38511yescharacteristic
629C22C37×#38611yescharacteristic
630C22C37×#38612yes—
631C22C37×#38611yescharacteristic
632C22C37×B(4,𝔽2)12yes—
633C22C37×#45812yes—
634C4—24no—
635C4—44no—
636C4—48no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C37×C22⋊#9511yescharacteristic
649C2C37×#179012yes—
650C2C37×#186712yes—
651C2C37×#188911yescharacteristic
652C2C37×#189011yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutatorC23C2×C42×C37
Frattini, cosocleC25C23×C37
prime radicalC23×D4×C37C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C25×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×C37×#342C2semidirect
5. C37×C22⋊#95C2semidirect
10. C37×#518C4semidirect
20. C2×#99×C37C4semidirect
22. C37×#386C4semidirect
46. C23×C4×C37C2×C4semidirect
72. C2×C22⋊C4×C37C2×C4semidirect
73. C2×C22⋊C4×C37C2×C4semidirect
152. C22×C4×C37C22⋊C4semidirect
200. C23×C37#95semidirect
258. C2×C4×C37#95semidirect
259. #10745C37direct (N × H)
316. C2×#342C2×C37semidirect
317. C22⋊#95C2×C37semidirect
336. #518C4×C37semidirect
346. C2×#99C4×C37semidirect
348. #386C4×C37semidirect
352. C37#10745direct (N × H)
373. C23×C4C2×C4×C37semidirect
399. C2×C22⋊C4C2×C4×C37semidirect
400. C2×C22⋊C4C2×C4×C37semidirect
479. C22×C4C22⋊C4×C37semidirect
527. C23#95×C37semidirect
585. C2×C4#95×C37semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C37×#5182
C22×#99×C372
C2×C37×#3862
C2×C37×#3422
C37×C22⋊#952
#1074537